PHASE DIaGRAM & PHASE RULE

MATERIAL SC (MM1101) ASSIGNMENT Submitted to - Dr. Ranjit Prasad

Presented by :- Shashank Karan : 2020UGCS023 Akhilesh Kumar Mishra : 2020UGCS053 Harsh Bajaj : 2020UGCS083 Ravi Kumar : 2020UGCS113

INTRODUCTION

Before, dip diving into the topic lets first know what is PHASE ?

¤ A phase can be defined as a homogeneous portion of a system that has uniform physical and chemical characteristics i.e. it is a physically distinct from other phases, chemically homogeneous and mechanically separable portion of a system.

For example Let consider H₂O : it exsits as ice in solid , water as liquid and vapour as a gas .

¤ Different phases or of same phase of different component can be mixed to form another substance with unique property these are called solution or mixture . These can liquid-liquid, liquid-solid, liquid-gas, solid-solid , solid-liquid, solid-gas, gas- liquid , gas-gas and gas-solid composition.

A solution (liquid or solid) is phase with more than one component; a mixture is a material with more than one phase

Here in the given chapter we would be discussing about the phase change , their transformation , their kinetics the set of rules describing their changes and ultimately going through one Phase Diagram of Iron- carbon System.

INTRODUCTION TO PHASE DIAGRAM

A diagram that depicts existence of different phases of a system under equilibrium is termed as Phase Diagram.

¤ It is actually a collection of solubility limit curves. It is also known as equilibrium or constitutional diagram.

¤ Equilibrium phase diagrams represent the relationships between temperature, compositions and the quantities of phases at equilibrium.

¤ These diagrams do not indicate the dynamics when one phase transforms into another.

¤ Useful terminology related to phase diagrams: liquidus, solidus, solvus, terminal solid solution, invariant reaction, , inter-metallic compound, etc.

¤ Phase diagrams are classified according to the number of component present in a particular system. Here is the naming, we will be discussing it later.

Single Component System – Unary Phase Diagram

Two Component System – Binary Phase Diagram

Three Component System – Tertiary Phase Diagram

Four Component System – Quarter Phase Diagram IMPORTANT TERMINOLOGY AND SOME FEATURES OF A PHASE DIAGRAM

1. LIQUIDUS -– The liquidus is the temperature at which an alloy is completely melted.

2. SOLIDUS - The solidus is the highest temperature at which an alloy is solid.

3.Terminal Solid Solution - Solid phases (α and β) that exist near the ends of phase diagrams are called terminal solid solutions .

4.Invariant Reaction Reaction that occurs under equilibrium conditions at a specific temperature and specific composition which can not be varied.

Important information, useful in materials development and selection, obtainable from a phase diagram:

- It shows phases present at different compositions and temperatures under slow cooling (equilibrium) conditions.

- It indicates equilibrium solid solubility of one element/compound in another.

- It suggests temperature at which an alloy starts to solidify and the range of solidification.

- It signals the temperature at which different phases start to melt.

- Amount of each phase in a two-phase mixture can be obtained.

Unary phase diagram

If a system consists of just one component (e.g.: water), equilibrium of phases exist is depicted by unary phase diagram. The component may exist in different forms, thus variables here are – temperature and pressure.

BINARY PHASE DIAGRAM

If a system consists of two components, equilibrium of phases exist is depicted by binary phase diagram.

For most systems, pressure is constant, thus independently variable parameters are – temperature and composition.

Two components can be either two metals (Cu and Ni), or a metal and a compound (Fe and Fe3C), or two compounds (Al2O3 and Si2O3), etc.

Two component systems are classified based on extent of mutual solid solubility – (a) completely soluble in both liquid and solid phases (isomorphous system) and (b) completely soluble in liquid phase whereas solubility is limited in solid state.

For isomorphous system - E.g.: Cu-Ni, Ag-Au, Ge-Si , Al2O3,etc.

GIBBS’S PHASE RULE

In 1875, Josiah Williard Gibbs published a general principle governing systems in the thermodynamic equilibrium called the Phase Rule in a paper tilted on the Equilibrium of Heterogeneous Substances .

“In a system under a set of conditions, number of phases (P) exist can be related to the number of components (C) and degrees of freedom (F)”

by Gibbs phase rule.

Where , Degrees of freedom refers to the number of independent variables (e.g.: pressure, temperature) that can be varied individually to effect changes in a system.

Thermodynamically derived Gibbs phase rule: P+F = C+2

In practical conditions for metallurgical and materials systems, pressure can be treated as a constant (1 atm.). Thus Condensed Gibbs phase rule is written as:

P+F = C+1 Hume-Ruthery conditions

Hume-Rothery rules, named after William Hume-Rothery, are a set of basic rules that describe the conditions under which an element could dissolve in a metal, forming a solid solution. There are two sets of rules; one refers to substitutional solid solutions, and the other refers to interstitial solid solutions.

For substitutional solid solutions, the Hume-Rothery rules are as follows:

1. The atomic radius of the solute and solvent atoms must differ by no more than 15%

( ) ( ) %difference = x 100% ( )

2. The crystal structures of solute and solvent must be similar. 3. Complete solubility occurs when the solvent and solute have the same valency. A metal is more likely to dissolve a metal of higher valency, than vice versa. 4. The solute and solvent should have similar electronegativity. If the electronegativity difference is too great, the metals tend to form intermetallic compounds instead of solid solutions. For interstitial solid solutions, the Hume-Rothery Rules are:

1. Solute atoms should have a smaller radius than 59% of the radius of solvent atoms. 2. The solute and solvent should have similar electronegativity. 3. Valency factor: two elements should have the same valence. The greater the difference in valence between solute and solvent atoms, the lower the solubility.

Fundamentally these are restricted to binary systems that form either substitutional or interstitial solid solutions. However, this approach limits assessing advanced alloys which are commonly multicomponent systems. Free energy diagrams (or phase diagrams) offer in-depth knowledge of equilibrium restraints in complex systems. LEVER’S RULE

The lever rule is a rule used to determine the mole fraction (xi) or the mass fraction (wi) of each phase of a binary equilibrium phase diagram. It can be used to determine the fraction of liquid and solid phases for a given binary composition and temperature that is between the liquidus and solidus line In an alloy or a mixture with two phases, α and β, which themselves contain two elements, A and B, the lever rule states that the mass fraction of the α phase is

a B a w = ( wb-wb ) /( wb ) where

a ● wb is the mass fraction of element B in the a phase b ● wb is the mass fraction of element B in the β phase ● wb is the mass fraction of element B in the entire alloy or mixture all at some fixed temperature or pressure. Procedure to find equilibrium relative amounts of phases (lever rule): - A tie-line is constructed across the two phase region at the temperature of the alloy to intersect the region boundaries. The relative amount of a phase is computed by taking the length of tie line from overall composition to the phase boundary for the other phase, and dividing by the total tieline length. In previous figure, relative amount of liquid and solid phases is given respectively by:

VARIENT REACTIONS

Observed triple point in unary phase diagram for water?

How about eutectic point in binary phase diagram?

These points are specific in the sense that they occur only at that particular conditions of concentration, temperature, pressure etc.

Try changing any of the variable, it does not exist i.e. phases are not equilibrium any more!

Hence they are known as invariant points, and represents invariant reactions.

Invariant reactions result in different product phases: terminal phases and intermediate phases. Intermediate phases are either of varying composition (intermediate solid solution) or fixed composition (intermetallic compound).

Occurrence of intermediate phases cannot be readily predicted from the nature of the pure components! Inter-metallic compounds differ from other chemical compounds in that the bonding is primarily metallic rather than ionic or covalent. E.g.: Fe3C is metallic, whereas MgO is covalent. When using the lever rules, inter-metallic compounds are treated like any other phase.

Fe-C binary system – Phase transformations

Fe-Fe3C phase diagram is characterized by five individual phases,: α–ferrite (BCC) Fe-C solid solution, γ-austenite (FCC) Fe-C solid solution, δ-ferrite (BCC) Fe-C solid solution, Fe3C (iron carbide) or cementite - an inter-metallic compound and liquid Fe-C solution and four invariant reactions:

- peritectic reaction at 1495 C and 0.16%C, δ-ferrite + L ↔ γ-iron (austenite)

- monotectic reaction 1495 C and 0.51%C, L ↔ L + γ-iron (austenite)

- eutectic reaction at 1147 C and 4.3 %C, L ↔ γ-iron + Fe3C (cementite) [ledeburite]

- eutectoid reaction at 723 C and 0.8%C, γ-iron ↔ α– ferrite + Fe3C (cementite) [pearlite]

Fe-C alloys CLASSIFICATION

Fe-C alloys are classified according to wt.% C present in the alloy for technological convenience as follows:

Commercial pure irons % C < 0.008 Low-carbon/mild steels 0.008 - %C - 0.3

Medium carbon steels 0.3 - %C - 0.8 High-carbon steels 0.8- %C - 2.11

Cast irons 2.11 < %C

Cast irons that were slowly cooled to room temperature consists of cementite, look whitish – white cast iron. If it contains graphite, look grayish – gray cast iron. It is heat treated to have graphite in form of nodules – malleable cast iron. If inoculants are used in liquid state to have graphite nodules – spheroidal graphite (SG) cast iron. Kinetics of nucleation and growth Nucleation and growth

• Structural changes / phase transformations takes place by nucleation followed by

growth.

• Temperature changes are important among variables (like pressure,

composition) causing phase transformations as diffusion plays important role.

• Two other factors that affect transformation rate along with temperature- (1) diffusion controlled rearrangement of atoms because of compositional and/or crystal structural differences; (2) difficulty encountered in nucleating small particles via change in surface energy associated with the interface.

Just nucleated particle has to overcome the positive energy associated with new interface form to survive and grow further. It does by reaching a critical size.

Homogeneous nucleation- Kinetics

• Homogeous nucleation- nucleation occurs within parent phase. All sites are of equal probability for nucleation. • It requires considerable under-cooling(cooling a material below the equilibrium temperature for a given transformation without the transformation occuring). • Free energy change associated with formation of new particle

∆f = 4/3πr³∆g + 4πr²¥

where r is radius of particle, ∆g is gibbs free energy per unit

volume and ¥ is surface energy of interface.

Critical value of particle size(which reduces with under-cooling) is given by

r* = -2¥/∆g or r* = 2¥Tm/∆Hf∆T

where Tm – freezing temperature(in K), Hf – latent heat of fusion ∆T –

amount of under-cooling at which nucleus is formed. Heterogeneous nucleation- Kinetics

In heterogeneous nucleation, the probability of nucleation occuring at certain preferred sites is much greater than that at other sites. E.g. : During solidification inclusion of foreign particles (inoculants), walls of container holding the liquid. In solid-solid transformation – foreign inclusions, grain boundaries, interfaces, stacking faults and dislocations. Considering, force equilibrium during second phase formation: When product particle makes only a point contact with the foreign surface, the foreign particle does not play any role in the nucleation process. ∆f*het=∆f*hom

• If the product particle completely wets the foreign surface, there is no

barrier for heterogeneous nucleation. ∆f*het= 0

• In intermediate conditions such as where the product particle attains

hemispherical shape. ∆f*het = ½ ∆f*hom

Growth Kinetics

• After formation of stable nuclei, growth of it occurs until equilibrium phase is being formed. • Growth occurs in two methods- thermal activated diffusion and controlled individual atom movement, or athermal collective movements of atoms. First one is more common than other. • Temperature dependance of nucleation rate(U), growth rate(I) and overall transformation rate(dX/dt) that is a function of both nucleation rate and growth rate i.e. dX/dt = fn(U,I):

● Time required for a transformation to completion has a reciprocal relationship to the overall transformation rate, C- curve(time- temperature-transformation or TTT diagram). • Transformation data are plotted as characteristic S – curve. • At small degrees of supercooling, where slow nucleation and rapid growth prevail, relatively coarse particles appear; at larger degrees of supercooling, relatively fine particles result.

PARTICLE STRENGTHENING BY PRECIPITATION REACTION Basic description

Methods have been devised to modify the yield strength, toughness of both crystalline and amorphous materials.These Strengthening mechanisms gives engineers the ability to tailor the mechanical properties of material to suit a very of different application.

Plastic deformation occur when large number of dislocation move and multiply as to result in microscope deformation. If we want to enhance materials Mechanical properties (i.e increase the yield and tensile strength)

We simply need to introduce a mechanism which prohibits the mobility of this location. whatever the mechanism may be(work hardening grain size reduction etc).They all hinder dislocation motion and render the material is stronger than previously.

The strength of material cannot infinitely increase. Each of mechanism explained below involve some trade off by which other material properties are compromised in the process of strengthening. Strengthening

● The ability of a metal to deform plastic lead depend on the ability of this location to move. ● Hardness and strength are related to how easily metal plastically deformed by reducing dislocation movement the mechanical strength can be improved. ● To the contrary if the dislocation movement is easy the metal will be soft easy to Deform. Strengthening Mechanism ● Grain size reduction ● Solid solution alloying ● Strain hardening ● Precipitation 1. Grain size reduction ● Grain boundaries are barriers to slip ● Barriers strength increase with misorisatation ● Smaller grain size more barriers to slip 2. Solid solution ● Impurity atoms distort the lattice and generate stress ● Streax can produce a barrier to dislocation motion

3.Strain hardening

● Room temperature deformation ● Common forming techniques used to change the cross sectional area 4.Precipitation

Precipitation hardening is a heat treatment technique that takes place in low temperature and makes use of following materials such as aluminium and titanium this cause increase yield strength as well as improved corrosion resistance depending on the alloying metals

● Metals Strengthening by precipitation reaction Precipitation hardening metal alloys the alloying element trapped in solution during quenching resulting in a soft material ageing a solutionised metals which allowed the following element to diffuse through the microstructure and form intermetallic particle. Which fall out of solution and increase the strength of alloys may age naturally at room temperature or artificially at elevated temperature . some naturally ageing can be prevented from age hardening until needed by storing at sub zero temperature.

During tempering alloys can be tempered after quenching by heating at temperature below the solutionising temperature.

During tempering the alloying element will diffuse through the alloy and react to form intermetallic compound. These precipitate out and form a small particle that strength the metal by impending the movement of this location through the crystal structure alloys.the mechanical properties of an a lawyer can be determined by careful control of the tempering time and temperature affecting the size and amount of precipitate. Artificially aged alloys are tempered at elevated temperature will naturally aging a lower may be tampered at room temperature. Some super alloys may be subjected to several tempering operation where a different party precipitate is formed during each operation this result in a large number of different precipitates that are difficult to drive back into solution this contributes to a high temperature strength of precipitation hardened super alloys.